Your style seems to be very simplified already so I'm not sure how much help I can give, but I'll try. You already seem to have a bit of a grasp of color theory looking at the colors you chose to shade with here, but I would say take it a step further. For black hair, you want to choose a color that is cool and deep, so I would say purples or blues would be the best colors to shade with depending on the color pallet of the piece.
